Standing Waves
Source: Arianna Brown, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA
Standing waves, or stationary waves, are waves that appear not to propagate and are produced by the interference of two waves traveling in opposite directions with the same frequency and amplitude. These waves appear to vibrate up and down with no linear movement and are most easily identified in vibrating finite media like a plucked guitar string, water in a lake, or air in a room. For example, if a string is fixed at both ends and two identical waves are sent traveling along the length, the first wave will hit the end barrier and reflect back in the opposite direction, and the two waves will superpose to produce a standing wave. This motion is periodic with frequencies defined by the length of the medium and is a visual example of simple harmonic motion. Simple harmonic motion is motion that oscillates or is periodic, where the restoring force is proportional to the displacement, meaning the farther something is pushed, the harder it pushes back.
The goal of this experiment is to understand the roles of wave superposition and reflection in creating standing waves, and exploit those concepts to calculate the first few resonant frequencies, or harmonics, of standing waves on a slinky. Each frequency that an object produces has its own standing wave patterns, where the wave with the lowest possible frequency is called the fundamental frequency. A harmonic is a wave that has a frequency proportionate to the fundamental frequency by whole integer numbers.
1. Observing the Superposition and Reflection of Slinky Pulses
- Stretch a slinky or steel spring lengthwise across a floor or hallway, with one student holding one end and another student holding the other. Use tape to mark two lengthwise 'barriers' about a foot away from the middle of the slinky, on each side. Repeat with barriers that are two feet away from the middle on each side.
- Take turns launching pulses (jerking the slinky a small distance horizontally and immediately snapping back to
| Harmonic (n) | # Cycles | Total Time (s) | Frequency (Hz) | f/f0 | Period (s) | Wavelength (m) |
| 1 | 10 | 19.2 | 0.521 (f0) | 1 | 1.210 | 16 m |
